Fictitious-Transfer Solutions in Cooperative Game Theory

Abstract

It is easy to see that games with transferable utility (TU) really are just a special case of games with nontransferable utility (NTU), because transfer activities can be remodeled as strategic options in a game “without transferable utility.” Thus, it is natural to ask why game theorists should have devoted substantial efforts to developing solution concepts for games with transferable utility. When I teach cooperative game theory now, more than 45 years after von Neumann and Morgenstern [1944], I try to motivate the old emphasis on coalitional games with transferable utility by two propositions. First, because coalitional interactions can be very complicated, we may initially want to simplify our analysis by assuming transferable utility, so that the set of feasible utility allocations for each coalition can be described by a single number. Second, by the method of fictitious transfers of weighted utility (or λ-transfers), we can easily generalize any solution concept for transferable-utility games to the case of games without transferable utility. Thus, from the perspective of 1990, the method of fictitious transfers appears to justify the original decision of von Neumann and Morgenstern [1944] to concentrate on games with transferable utility. However, the method of fictitious transfers was recognized only after the pivotal breakthrough of Harsanyi [1963]. My purpose in this paper is to reexamine the importance of this method, in the context of the history of its development and some recent results.